HomeCalculatorsPhysicsHydraulic Diameter Calculator
Physics calculator

Hydraulic Diameter Calculator

Compute hydraulic diameter D_h=4A/P_w for a general section, a full circular pipe, a closed rectangular duct, or an annulus. Runs locally. Not Q=Av, not Manning, and not Darcy.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 15/15 tests · Production surface contract 3/3 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Hydraulic diameter D_h=4A/P_w for a general section, full circular pipe, closed rectangular duct, or concentric annulus.
Scope
D_h = 4 A / P_w; R = A / P_w = D_h / 4
Verification
Engine tested · 15/15 tests · Production surface contract 3/3 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
Sources
Evidence
2 golden · 8 boundary · 5 property · Production surface contract 3/3 · Artifact integrity PASS
Production
Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 163 CURRENT) @ 2026-09-17T06:27:56.932Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

GeneralD_h = 4 A / P_w
CircularD_h = D
Rectangular ductD_h = 2 a b / (a + b)
iSI. P_w is the wetted perimeter. Closed rectangular duct wets all four walls. This page is not Q=Av, not Manning discharge, not Reynolds, and not Darcy–Weisbach.

How to use

1

Choose the section

General uses area and wetted perimeter. Circular is a full pipe. Rectangular is a closed duct. Annulus is concentric tubes. This is not Q=Av.

2

Enter geometry

General: A and Pw (or R). Circular: D. Rectangular: a and b. Annulus: D_o and D_i with D_i < D_o.

3

Read D_h

Hydraulic diameter is in m. R = D_h/4.

Example calculations

Common configurations with formula and result.

ϟ

Section A=0.01 m², Pw=0.4 m

General 4A/P_w

D_h = 4 A / P_w
D_h=0.1 m · R=0.025 m
ϟ

Full pipe D=0.1 m

Circular flowing full

D_h = D
D_h=0.1 m

Hydraulic Diameter calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
D_h = 4 A / P_w. Circular full pipe: D_h = D. Closed rectangular duct: D_h = 2ab/(a+b). Annulus: D_h = D_o − D_i. R = D_h/4.
What it calculates
Hydraulic diameter D_h=4A/P_w for a general section, full circular pipe, closed rectangular duct, or concentric annulus.
Inputs
  • mode?
  • A|Pw|R|Dh
  • D
  • a,b
  • D_o,D_i
Outputs
  • Dh
  • R
  • A?
  • Pw?
Formula
D_h = 4 A / P_w
Assumptions
  • D_h = 4 A / P_w; R = A / P_w = D_h / 4
  • Full circular pipe: D_h = D; closed rectangular duct: D_h = 2ab/(a+b); annulus: D_h = D_o − D_i
  • Not Q=Av, not Manning Q, not Reynolds, not Darcy, not a weir or orifice
Units
  • SI; lengths in m; area in m²
Boundary conditions
  • missing A+Pw, R, circular D, rectangular a+b, or annular D_o+D_i → MISSING_REQUIRED_INPUT
  • A, Pw, R, D, a, b, D_o, or D_i ≤ 0 → VALUE_MUST_BE_POSITIVE
  • annulus D_i ≥ D_o → VALUE_OUT_OF_RANGE
  • A+Pw+R, R+Dh, Q, v, n, f, C_d, or NPSH/pump fields → MIXED_INPUT_ENCODING
  • manning, flow, reynolds, darcy, weir, orifice, pump, or NPSH as mode → INVALID_MODE
Example
A=0.01 Pw=0.4 → D_h=0.1 m
Validation cases

3 published on this page · 15/15 tests · Production surface contract 3/3 · View evidence

  • A=0.01 Pw=0.4 → Dh=0.1
  • mode=circular D=0.1 → Dh=0.1
  • A=0.01 Pw=0.4 Q=0.02 → MIXED_INPUT_ENCODING
Sources
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute hydraulic diameter D_h = 4A/P_w.

Supported and not supported

Supported — general A and P_w · invert from R or D_h · full circular pipe · closed rectangular duct · concentric annulus · API physics.fluid.hydraulic_diameter

Not supported — Q=Av identities, Manning discharge, Reynolds number, Darcy–Weisbach, weir, orifice, open-channel rectangular as a silent duct formula

Agent / API notes

Capability id: physics.fluid.hydraulic_diameter · tool id: hydraulic-diameter · pin 1.0.0.

{ "A": 0.01, "Pw": 0.4 }

Circular: { "mode": "circular", "D": 0.1 }. Rectangular: { "mode": "rectangular", "a": 0.2, "b": 0.1 }. Annulus: { "mode": "annular", "D_o": 0.1, "D_i": 0.06 }. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/hydraulic-diameter. There is no /calc/fluid.

Other calculators in this family: Flow rate, Reynolds number, Manning formula .

Q Flow rate › Re Reynolds number › n Manning formula ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this Q = A·v?

No. Volumetric flow from area and velocity is /calc/physics/flow-rate. Sending Q or v is MIXED_INPUT_ENCODING.

Is this Manning?

No. Manning uses R=A/P in Q=(1/n)A R^{2/3} S^{1/2} at /calc/physics/manning-formula. This page stops at D_h and R. Sending n or S is MIXED_INPUT_ENCODING.

Is a rectangular duct the same as an open channel?

No. Closed-duct mode wets 2(a+b). An open rectangular channel would wet a+2b; give A and Pw in general mode for that.

Where does this run?

Locally in the browser by default. REST and MCP call the same fluid-engine hydraulicDiameter wrapper.